Many consumer electronic devices have outer enclosures and coverings that give the enclosures and coverings an aesthetically pleasing look and feel. Some enclosures and coverings have curved surfaces that add to the aesthetic appeal of the device. Often, the enclosures and coverings undergo finishing operations in order to impart distinctive characteristics to the enclosures and coverings. For example, surfaces can be texturized to give the enclosures and coverings a matte look and feel. Other times, the surfaces are polished to a mirror shine. The finishing process can also remove surface defects that would otherwise be visible and detract from the aesthetic appeal of the enclosure or covering.
One challenge associated with finishing curved surfaces is that it can be difficult to follow a contour of a curved surface using conventional finishing techniques. For example, it can be difficult to control fine movement of a flat sanding belt or round abrasive wheel over curved edges and corners of a part. The resultant part can have an uneven finish at the curved edges and corners. It can be especially difficult to control the finishing process if the curved surface has a complex three-dimensional shape, such as a spline shape.